Method for calculating voltage loss of fuel cell and system performing the same

ABSTRACT

A method for calculating voltage loss of a fuel cell is provided. The method includes sensing an open circuit voltage that is generated in a stack when the switch is opened and detecting an operation voltage and an operation current that are generated in the stack when the switch is closed. A first change graph of voltage data over time is calculated using the voltage data and current data from a time when the switch is opened in a state where the switch is closed. A first voltage of a point at which a trend line for an interval where the voltage data linearly varies with the time meets the first change graph is sensed and then an ohmic resistance voltage loss is calculated using a difference between the first voltage and the operation voltage.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2017-0149123 filed on Nov. 10, 2017, the entirecontents of which are incorporated herein by reference.

BACKGROUND (a) Field of the Invention

The present invention relates to a method for calculating voltage lossof a fuel cell and a system performing the method to calculate a voltageloss due to an active resistance, a voltage loss due to an ohmicresistance, and a voltage loss due to a mass transfer resistance in afuel cell system including a stack that generates power using air andhydrogen.

(b) Description of the Related Art

It is necessary to measure a voltage loss and to characterize aresistance component to determine a degree of deterioration ofperformance of a fuel cell stack and to accurately determine a cause ofdeterioration. Resistance measurement using alternating current (AC)impedance, measurement of high frequency resistance (HFR) using analternating current (AC) milliohm meter, and measurement of ohmicresistance using a current cutoff method are widely used to measure aresistance characteristic of the fuel cell stack or a unit cell of afuel cell.

FIG. 1 is a graph showing a typical voltage loss according to therelated art. Referring to FIG. 1, a horizontal axis of the graphrepresents current density (mA/cm²), a vertical axis of the graphrepresents the cell voltage, and a total voltage loss of the fuel cellunder operation is composed of various components.

Although resistance measurement method using AC impedance is widely usedfor separating or obtaining components of voltage loss and eachresistance component, a substantial amount of time is required tomeasure impedance of wide band (e.g., several tens kHz to several MHz)and perform equivalent circuit modeling and nonlinear analysis in theresistance measurement method using AC impedance. Additionally, tomeasure all the resistance components of each cell constituting thestack using the impedance measurement, it is necessary to sequentiallytest all the cells or equipment for simultaneously inputting alternatingcurrent to the cells to be measured. Thus, composition of equipment forthe resistance measurement method using AC impedance becomes complex anda cost for performing the resistance measurement method increases.

A developed simplified method is a resistance measurement method usingthe AC milliohm meter and the current cutoff method. However, thesemethods have a rapid measurement time (e.g., a few seconds) but measureonly the ohmic resistance and do not measure the remaining resistancecomponents (i.e., the active resistance and the mass transferresistance). Thus, it is difficult to identify a cause of performancedeterioration of the fuel cell stack and the cell.

The above information disclosed in this section is merely forenhancement of understanding of the background of the invention andtherefore it may contain information that does not form the prior artthat is already known in this country to a person of ordinary skill inthe art.

SUMMARY

The present invention provides a method for calculating voltage loss ofa fuel cell and a system performing the same that are capable ofeffectively and rapidly calculating a voltage loss due to an activeresistance, a voltage loss due to an ohmic resistance, and a voltageloss due to a mass transfer resistance to more easily determine a degreeof deterioration of the fuel cell.

An exemplary embodiment of the present invention provides the method forcalculating voltage loss of the fuel cell that includes a stackincluding cells, a power load using a current and a voltage generated inthe stack, a monitoring terminal connected to the cells to sense thecurrent and the voltage, a switch provided on a circuit that connectsthe power load and the stack, and a controller configured to executeoperations of the switch and the stack. The method may include sensing,by the controller, an open circuit voltage generated in the stack whenthe switch is opened; detecting, by the controller, an operation voltageand a operation current generated in the stack when the switch isclosed; calculating, by the controller, a first change graph of voltagedata over time using the voltage data and current data from a time whenthe switch is opened in a state where the switch is closed, and sensinga first voltage of a point at which a trend line for an interval wherethe voltage data linearly varies with the time meets the first changegraph; and calculating, by the controller, an ohmic resistance voltageloss using a difference value between the first voltage and theoperation voltage.

The method for calculating voltage loss of the fuel cell may furtherinclude: calculating, by the controller, a second change graph of thevoltage data over square root of the time, and calculating a secondvoltage of a point at which a trend line for an interval where thevoltage data linearly varies with the square root time meets the secondchange graph; and calculating, by the controller, a mass transferresistance voltage loss using a difference value between the opencircuit voltage and the second voltage.

Additionally, the method may include: calculating, by the controller, anactive resistance voltage loss by subtracting the mass transferresistance voltage loss and the ohmic resistance voltage loss from theopen circuit voltage. The controller may be configured to measurechanges in the voltage data and the current data with respect to thetime in a predetermined time unit using an oscilloscope or a datarecorder connected to the monitoring terminal.

Another exemplary embodiment of the present invention provides themethod for calculating voltage loss of the fuel cell that includes astack including cells, a power load using a current and a voltagegenerated in the stack, a monitoring terminal connected to the cells tosense the current and the voltage, a switch provided on a circuit thatconnects the power load and the stack, and a controller configured toexecute operations of the switch and the stack. The method may includesensing, by the controller, an open circuit voltage generated in thestack when the switch is opened; calculating, by the controller, a firstchange graph of voltage data over time using the voltage data andcurrent data generated from a time when the switch is closed in a statewhere the switch is opened, and sensing a highest first voltage in aninterval where the voltage data linearly varies with the time;detecting, by the controller, an operation voltage generated in thestack when the switch is closed; and calculating, by the controller, anohmic resistance voltage loss using a difference value between thehighest first voltage and the operation voltage.

The method for calculating voltage loss of the fuel cell may furtherinclude: calculating, by the controller, a second change graph of thevoltage data over square root of the time, and calculating a lowestsecond voltage in an interval where the voltage data linearly varieswith the square root time; and calculating, by the controller, a masstransfer resistance voltage loss using a difference value between theopen circuit voltage and the lowest second voltage. In addition, themethod may include: calculating, by the controller, an active resistancevoltage loss by subtracting the mass transfer resistance voltage lossand the ohmic resistance voltage loss from the open circuit voltage.

Another exemplary embodiment of the present invention may provide themethod for calculating voltage loss of a power supply that includes apower load using a current and a voltage generated in the power supply,a monitoring terminal connected to the power supply to sense the currentand the voltage, a switch provided on a circuit that connects the powerload and the power supply, and a controller configured to executeoperations of the switch and the power supply. The method may includesensing, by the controller, an open circuit voltage generated in thepower supply when the switch is opened; sensing, by the controller, anoperation voltage and a operation current generated in the power supplywhen the switch is closed; calculating, by the controller, a firstchange graph of voltage data over time using the voltage data andcurrent data from a time when the switch is opened in a state where theswitch is closed, and sensing a highest first voltage that correspondsto a point at which a trend line for an interval where the voltage datalinearly varies with the time meets the first change graph; andcalculating, by the controller, an ohmic resistance voltage loss using adifference value between the highest first voltage and the operationvoltage.

The method may further include: calculating, by the controller, a secondchange graph of the voltage data over square root of the time, andcalculating a lowest second voltage that corresponds to a point at whicha trend line for an interval where the voltage data linearly varies withthe square root time meets the second change graph; and calculating, bythe controller, a mass transfer resistance voltage loss using adifference value between the open circuit voltage and the lowest secondvoltage. In addition, the method may include: calculating, by thecontroller, an active resistance voltage loss by subtracting the masstransfer resistance voltage loss and the ohmic resistance voltage lossfrom the open circuit voltage. The controller may be configured tomeasure changes in the voltage data and the current data with respect tothe time in a predetermined time unit using an oscilloscope or a datarecorder connected to the monitoring terminal.

Another exemplary embodiment of the present invention may provide themethod for calculating voltage loss of the power supply that includes apower load using a current and a voltage generated in the power supply,a monitoring terminal connected to the power supply to sense the currentand the voltage, a switch provided on a circuit that connects the powerload and the power supply, and a controller configured to executeoperations of the switch and the power supply. The method may includesensing, by the controller, an open circuit voltage generated in thestack when the switch is opened; calculating, by the controller, a firstchange graph of voltage data over time using the voltage data andcurrent data generated from a time when the switch is closed in a statewhere the switch is opened, and sensing a highest first voltage in aninterval where the voltage data linearly varies with the time; sensing,by the controller, an operation voltage generated in the stack when theswitch is closed; and calculating, by the controller, an ohmicresistance voltage loss using a difference value between the highestfirst voltage and the operation voltage.

The method for calculating voltage loss of the fuel cell may furtherinclude: calculating, by the controller, a second change graph of thevoltage data over square root of the time, and calculating a lowestsecond voltage in an interval where the voltage data linearly varieswith the square root time; and calculating, by the controller, a masstransfer resistance voltage loss using a difference value between theopen circuit voltage and the lowest second voltage. The method may alsoinclude: calculating, by the controller, an active resistance voltageloss by subtracting the mass transfer resistance voltage loss and theohmic resistance voltage loss from the open circuit voltage.

An exemplary embodiment of the present invention provides the systemperforming the method for calculating voltage loss of the fuel cell thatmay include: a stack including cells; a power load using a current and avoltage generated in the stack; a monitoring terminal connected to thecells to sense the current and the voltage; a switch provided on acircuit that connects the power load and the stack; and a controllerconfigured to execute operations of the switch and the stack, sense anopen circuit voltage generated in the stack when the switch is opened,detect an operation voltage and a operation current generated in thestack in a state where the switch is closed, calculate a first changegraph of voltage data over time using the voltage data and current datafrom a time when the switch is opened when the switch is closed, sense afirst voltage of a point at which a trend line for an interval where thevoltage data linearly varies with the time meets the first change graph,and calculate an ohmic resistance voltage loss using a difference valuebetween the first voltage and the operation voltage.

The controller may be configured to calculate a second change graph ofthe voltage data over square root of the time, calculate a secondvoltage of a point at which a trend line for an interval where thevoltage data linearly varies with the square root time meets the secondchange graph, and calculate a mass transfer resistance voltage lossusing a difference value between the open circuit voltage and the secondvoltage. The controller may further be configured to calculate an activeresistance voltage loss by subtracting the mass transfer resistancevoltage loss and the ohmic resistance voltage loss from the open circuitvoltage. Additionally, the controller may be configured to measurechanges in the voltage data and the current data with respect to thetime in a predetermined time unit using an oscilloscope or a datarecorder connected to the monitoring terminal.

Another exemplary embodiment of the present invention provides thesystem performing the method for calculating voltage loss of the fuelcell that may include: a stack including cells; a power load using acurrent and a voltage generated in the stack; a monitoring terminalconnected to the cells to sense the current and the voltage; a switchprovided on a circuit that connects the power load and the stack; and acontroller configured to execute operations of the switch and the stack,to sense an open circuit voltage generated in the stack when the switchis opened, to calculate a first change graph of voltage data over timeusing the voltage data and current data generated from a time when theswitch is closed in a state where the switch is opened, to sense ahighest first voltage in an interval where the voltage data linearlyvaries with the time, to detect an operation voltage generated in thestack when the switch is closed, and to calculate an ohmic resistancevoltage loss using a difference value between the highest first voltageand the operation voltage.

The controller may be configured to calculate a second change graph ofthe voltage data over square root of the time, to calculate a lowestsecond voltage in an interval where the voltage data linearly varieswith the square root time, to calculate a mass transfer resistancevoltage loss using a difference value between the open circuit voltageand the lowest second voltage, and to calculate an active resistancevoltage loss by subtracting the mass transfer resistance voltage lossand the ohmic resistance voltage loss from the open circuit voltage. Themethod for calculating voltage loss of the fuel cell according to theexemplary embodiment of the present invention may effectively andrapidly calculate the voltage loss due to the active resistance, thevoltage loss due to the ohmic resistance, and the voltage loss due tothe mass transfer resistance by using a change characteristic of anelectric current and a voltage generated by closing or opening a switchdisposed between the stack and the power load.

Further, a charge step method according to an exemplary embodiment ofthe present invention may minimize or reduce a change of an operationstate of the fuel cell by reducing the switch opening and closing timeto within a few seconds. Thus, the exemplary embodiment of the presentinvention may suppress deformation and deterioration of the cell or thestack due to a thermal shock during measurement of a characteristic ofthe fuel cell, and according to the exemplary embodiment of the presentinvention, it is not necessary to stop or restart a load operation ofthe fuel cell during measurement of the characteristic of the fuel cell.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure will now bedescribed in detail with reference to certain exemplary embodimentsthereof illustrated the accompanying drawings which are givenhereinbelow by way of illustration only, and thus are not limitative ofthe present disclosure, and wherein:

FIG. 1 is a graph showing a typical voltage loss according to therelated art;

FIG. 2 is a schematic configuration diagram of a fuel cell systemaccording to an exemplary embodiment of the present invention;

FIG. 3 is a graph showing a relationship of a current and a voltage overtime in the fuel cell system according to an exemplary embodiment of thepresent invention;

FIG. 4 is a graph showing in detail the relation of the current and thevoltage according to time t in the fuel cell system according to anexemplary embodiment of the present invention;

FIG. 5 is a graph showing a voltage over time t in the fuel cell systemaccording to an exemplary embodiment of the present invention;

FIG. 6 is a graph showing a voltage over time (√{square root over (t)})in the fuel cell system according to an exemplary embodiment of thepresent invention;

FIG. 7 is a flowchart showing a method for calculating a voltage loss ofa fuel cell according to an exemplary embodiment of the presentinvention;

FIG. 8 is a graph showing a relationship between a current and a voltageof the fuel cell over time when a switch is opened from a closed stateaccording to an exemplary embodiment of the present invention; and

FIG. 9 is a graph showing a relationship between a current and a voltageof the fuel cell over time when the switch is closed from an openedstate according to an exemplary embodiment of the present invention.

DETAILED DESCRIPTION

It is understood that the term “vehicle” or “vehicular” or other similarterm as used herein is inclusive of motor vehicles in general such aspassenger automobiles including sports utility vehicles (SUV), buses,trucks, various commercial vehicles, watercraft including a variety ofboats and ships, aircraft, and the like, and includes hybrid vehicles,electric vehicles, plug-in hybrid electric vehicles, hydrogen-poweredvehicles and other alternative fuel vehicles (e.g. fuels derived fromresources other than petroleum). As referred to herein, a hybrid vehicleis a vehicle that has two or more sources of power, for example bothgasoline-powered and electric-powered vehicles.

Although exemplary embodiment is described as using a plurality of unitsto perform the exemplary process, it is understood that the exemplaryprocesses may also be performed by one or plurality of modules.Additionally, it is understood that the term controller/control unitrefers to a hardware device that includes a memory and a processor. Thememory is configured to store the modules and the processor isspecifically configured to execute said modules to perform one or moreprocesses which are described further below.

Furthermore, control logic of the present invention may be embodied asnon-transitory computer readable media on a computer readable mediumcontaining executable program instructions executed by a processor,controller/control unit or the like. Examples of the computer readablemediums include, but are not limited to, ROM, RAM, compact disc(CD)-ROMs, magnetic tapes, floppy disks, flash drives, smart cards andoptical data storage devices. The computer readable recording medium canalso be distributed in network coupled computer systems so that thecomputer readable media is stored and executed in a distributed fashion,e.g., by a telematics server or a Controller Area Network (CAN).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations of one or more of the associatedlisted items.

Unless specifically stated or obvious from context, as used herein, theterm “about” is understood as within a range of normal tolerance in theart, for example within 2 standard deviations of the mean. “About” canbe understood as within 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0.5%,0.1%, 0.05%, or 0.01% of the stated value. Unless otherwise clear fromthe context, all numerical values provided herein are modified by theterm “about.”

An exemplary embodiment of the present invention will hereinafter bedescribed in detail with reference to the accompanying drawings. Thesizes and thicknesses of the configurations shown in the drawings areprovided selectively for the convenience of description, such that thepresent invention is not limited to those shown in the drawings and thethicknesses are exaggerated to make some parts and regions clear.

However, parts which are not related with the description are omittedfor clearly describing the exemplary embodiment of the presentinvention, and like reference numerals refer to like or similar elementsthroughout the specification. In the following description, dividingnames of components into first, second, and the like is to divide thenames because the names of the components are the same as each other,and an order thereof is not particularly limited.

FIG. 2 is a schematic configuration diagram of a fuel cell systemaccording to an exemplary embodiment of the present invention. Referringto FIG. 2, a fuel cell (or the fuel cell system) 10 that is a powersupply system or an electric power source may include a stack 200 havinga plurality of cells 100, a monitoring terminal 500, a switch 400, apower load (e.g., an electronic load) 300, and a control unit (or acontroller) 600. An oscilloscope 700 and a data recorder 800 may beconnected or coupled to the fuel cell system 10.

In particular, the power load 300 may consume an electrical energygenerated from the stack 200 and may include a driving motor configuredto drive a vehicle and an electrical component (e.g., the electricalcomponent of the vehicle). The switch 400 may be provided or disposed ona circuit, which electrically connects the stack 200 and the power load300, to supply a current or a voltage generated in the stack 200 to thepower load 300 or to block the current or the voltage from the stack. Anelectric power of the stack 200 may be supplied to the power load 300when the switch 400 is closed, and the electric power may be blockedwhen the switch is opened.

The oscilloscope 700 and the data recorder 800 may be configured tomeasure a change in a voltage and a current generated in a cell 100 orthe stack 200 in units of several tens of nanometers to several hundredsof microseconds. The oscilloscope 700 and the data recorder 800 may beconfigured to measure the voltage and the current of the stack 200 orthe cell 100 when an operation state of the fuel cell system is changed.The controller 600 may be configured to execute an operation of the fuelcell 10. In particular, the controller 600 may be configured to transmitand receive a signal to and from the oscilloscope 700 and the datarecorder 800 to calculate each resistance component and a voltage lossdue to each resistance component using the received current value or thereceived voltage value. The controller 600 may then be configured tooperate the fuel cell system based on the calculated ohmic resistancevoltage loss.

An exemplary embodiment of the present invention may use a charge stepmethod to measure a voltage loss of the stack 200 or the cell 100 and toderive a voltage loss through each resistance component (i.e., ohmicresistance, active resistance (or activation resistance), and masstransfer resistance). The stack 200 may include the cells 100 and mayhave a structure in which a potential difference is generated betweenboth electrodes when hydrogen is supplied to an anode of the stack andair is supplied to a cathode of the stack. The stack 200 may generate anopen circuit voltage when the switch 400 is opened and may generate aclosed circuit voltage when the switch 400 is closed.

In an exemplary embodiment of the present invention, an electric powerproduced by the fuel cell stack 200 may vary based on an amount ofcurrent required by the power load 300. When performance of the cell 100or the stack 200 is evaluated to determine a characteristic of the cellor the stack, the charge step method may be performed as a method ofmeasuring the voltage loss and the resistance and may use current andvoltage variations of the cell or the stack. For example, the controller600 may be one or more microprocessors operated by a program or hardwareincluding the microprocessor. The program may include a series ofcommands for executing the method according to the exemplary embodimentof the present invention, which will be described below. The commandsmay be stored in a memory.

FIG. 3 is a graph showing a relationship of a current and a voltage overtime in the fuel cell system according to an exemplary embodiment of thepresent invention. Referring to FIG. 3, a horizontal axis of the graphrepresents time and a vertical axis of the graph represents voltage andcurrent. When the switch 400 is opened and closed for a short period oftime while the cell 100 or the stack 200 of the fuel cell is operatingat a constant current I₀ and a constant voltage V₀, a current of thefuel cell may be instantaneously interrupted and the current maysequentially change in a step form of I₀, I₁, and I₀. The current I₁ mayhave a value of 0 ampere. The voltage may sequentially change in a stepform of V₀, V₁, and V₀ when the current changes stepwise. When the timefor opening and closing the switch 400 is short, the voltage change mayappear in a form of a pulse as shown in FIG. 3. The voltage V₁ mayapproach an open circuit voltage Vocv when a time for opening the switch400 increases.

The charge step method according to the exemplary embodiment of thepresent invention may minimize a change of an operating state of thefuel cell 10 by decreasing the opening and closing time of the switch400 to within a few seconds. Thus, the exemplary embodiment of thepresent invention may suppress deformation and deterioration of the cell100 or the stack 200 due to a thermal shock during measurement of acharacteristic of the fuel cell, and according to the exemplaryembodiment of the present invention, it is not necessary to stop orrestart an operation of the fuel cell during measurement of thecharacteristic of the fuel cell.

FIG. 4 is a graph showing in detail the relationship of the current andthe voltage according to time t in the fuel cell system according to anexemplary embodiment of the present invention. FIG. 4 shows avoltage-time curve obtained by extending a period between t₀ and t₁ inFIG. 3 to several milliseconds.

It may be possible to obtain information necessary for the charge stepmethod by observing the voltage change using the oscilloscope 700 or thehigh-speed data recorder 800 in the period between t₀ and t₁ when theoperation voltage V₀ changes by opening and closing the switch 400. Theto denotes a time when the switch 400 is opened (e.g., a circuitbreaking time), and the t₁ denotes a time when the switch 400 is closedagain (e.g., a circuit connection time). To execute the charge stepmethod, the period between t₀ and t₁ may be 1 second.

As shown in FIG. 4, the voltage of the fuel cell 100 or the stack 200may sharply increase at a time point to when the switch 400 is opened.This sudden voltage change may mean that the voltage loss caused by theohmic resistance is linearly recovered when the current is removed. Whenthe voltage loss due to the ohmic resistance is fully recovered, thevoltage losses due to the activation and mass transfer resistances maybe sequentially recovered and may appear to be in a nonlinear form.

FIG. 5 is a graph showing a voltage over time t in the fuel cell systemaccording to an exemplary embodiment of the present invention. Inparticular, FIG. 5 shows a voltage-time curve obtained by extending orenlarging the voltage-time curve of FIG. 4 to several tens to severalhundreds of microseconds. When the current is instantaneously cut off bythe charge step method, the voltage loss due to the ohmic resistance maybe restored to linearly restore the voltage for a very short period oftime. The voltage loss due to the ohmic resistance may be usuallyrecovered within several tens to several hundreds of microseconds. Atrend line for an interval where the voltage linearly varies with timemay be created using linear regression analysis. The voltage loss−V_(ohmic)=(V_(A)−V₀) due to the ohmic resistance may be obtained usinga point A at which the trend line meets the voltage-time curve.

FIG. 5 shows a nonlinear voltage recovery curve after t₂ showing therecovery of the voltage loss caused by the activation and mass transferresistances. The following equation {1} may determine a relationship ofa recovery of the activation resistance voltage loss (ΔVact) accordingto an oxidation-reduction reaction by electrons and the time. Forexample, τ_(c) in the equation {1} may be a constant. The followingequation {2} may determine a relationship of a recovery of the masstransfer resistance voltage loss (ΔVmt) according to gas diffusion andthe time.

$\begin{matrix}{{\ln \left( {\Delta \; V_{act}} \right)} \propto \frac{t}{\tau_{c}}} & \left\{ 1 \right\} \\{{\Delta \; V_{mt}} \propto \sqrt{t}} & \left\{ 2 \right\}\end{matrix}$

FIG. 6 is a graph showing a voltage over square root of time (√{squareroot over (t)}) in the fuel cell system according to an exemplaryembodiment of the present invention. Referring to FIG. 6, after a squareroot t₃ (√{square root over (t₃)}) time point where the recovery of thevoltage losses due to the ohmic resistance and the activation resistanceis completed, a relation of the voltage and the square root time(√{square root over (t)}) may linearly change as shown in the equation{2}.

A trend line for an interval where the voltage linearly varies with thesquare root time may be generated using linear regression analysis. Thevoltage loss −V_(mt)=(V_(OCV)−V_(B)) due to the mass transfer resistancemay be obtained using a point B where the trend line meets thevoltage-square root time curve. As expressed by the following equation{3}, the voltage loss V_(act) may be obtained using a relationship of atotal voltage loss −V and −V_(ohmic) and −Vmt. The total voltage loss −Vmay be obtained from a difference between the open circuit voltageV_(ocv) of the fuel cell and the steady state load operation voltage V₀.

ΔV _(act) =ΔV−V _(ohmic) +ΔV _(mt))  (3)

The ohmic resistance, the mass transfer resistance, and the activationresistance may be obtained by dividing each voltage loss value obtainedby the above method by the operation current I₀.

FIG. 7 is a flowchart showing a method for calculating a voltage loss ofthe fuel cell according to an exemplary embodiment of the presentinvention. A step S700 may include sufficient preprocessing to start atest of the fuel cell under a normal operating condition and a step ofmeasuring and recording the open circuit voltage V_(OCV) of thepreprocessed fuel cell. A step S710 may include the load operation ofthe fuel cell in the steady state. In the step S710, the voltage valueV₀ stabilized under the current value I₀ may be measured and recorded.The steady state may include a condition in which a voltage V₀±5 mVmaintains for several minutes under the current I₀.

A step S720 may be a step of sensing or detecting a voltage and acurrent of the fuel cell 10 operating in the steady state at apredetermined time interval using the oscilloscope 700 or the high-speeddata recorder 800 before opening and closing the switch 400. The datarecording interval may be set in a range of tens to hundreds ofmicroseconds. A step S730 may be a step of recording the voltage and thecurrent of the fuel cell at a predetermined time interval using theoscilloscope 700 or the high-speed data recorder 800 and ofsimultaneously opening and closing the switch 400 to generateinstantaneous current interruption in the fuel cell operating state.

As shown in FIG. 5, a step S740 may be a step of collecting voltage-timedata using the oscilloscope 700 or the high-speed data recorder 800,performing a linear regression analysis on an initial linear interval ofthe voltage-time curve corresponding to the voltage-time data, andobtaining the voltage loss V_(ohmic) due to the ohmic resistance from anintersection of the trend line and the voltage-time curve.

As shown in FIG. 6, a step S750 may be a step of collectingvoltage-square root time data using the oscilloscope 700 or thehigh-speed data recorder 800, performing a linear regression analysis onan linear interval of the voltage-square root time curve correspondingto the voltage-square root time data, and obtaining the voltage lossV_(mt) due to the mass transfer resistance from an intersection of thetrend line and the voltage-square root time curve.

A step S760 may be a step of calculating the voltage loss V_(act) due tothe active resistance using the V_(OCV) obtained from the step S700, theV₀ obtained from the step S710, the V_(ohmic) obtained from the stepS740, the V_(mt) obtained from the step S750, and the equation {3}.

FIG. 8 is a graph showing a relationship between a current and a voltageof the fuel cell over time when the switch is opened from a closed stateaccording to an exemplary embodiment of the present invention. FIG. 8shows changes of the current and the voltage over time when the chargestep method is applied to the fuel cell 10 that is in a normaloperation. When the switch 400 is opened while the cell 100 or the stack200 of the fuel cell is operating at a constant current I₀ and at aconstant voltage V₀, a current of the fuel cell may be instantaneouslyinterrupted so that the current sequentially changes in a step form ofI₀ and I₁. The current I₁ may have a value of 0 ampere.

When an opening time (e.g., several tens of seconds to several minutes)of the switch 400 is substantial, the voltage of the fuel cell may berestored to the open circuit voltage Vocv. A method of obtaining thevoltage loss due to the ohmic resistance, the mass transfer resistance,and the activation resistance is the same as or similar to the methoddescribed with reference to FIGS. 5 and 6. When the method is used, aresult of the linear regression analysis for creating the linear trendline from the voltage-square root time graph may be more accurate. Themethod may be used when the load has to be completely removed from thefuel cell due to maintenance or malfunction of the fuel cell.

FIG. 9 is a graph showing a relationship between a current and a voltageof the fuel cell over time when the switch is closed from an openedstate according to an exemplary embodiment of the present invention.FIG. 9 shows changes of the current and the voltage over time when thecharge step method is applied to the fuel cell 10 that is in a standbystate.

When the switch 400 is closed while a voltage across the cell 100 or thestack 200 of the fuel cell is an open circuit voltage V₁ and a currentthrough the cell or the stack is blocked, the current may sequentiallychange in a step form of I₀ to I₁. The current I₁ may be maintained at aconstant value. When the switch is connected or closed for several tensof seconds to several minutes, the voltage may be stabilized to aconstant value such as V_(I).

A method of obtaining the voltage loss due to the ohmic resistance, themass transfer resistance, and the activation resistance is the same asor similar to the method described with reference to FIGS. 5 and 6. Thismethod may be utilized when the fuel cell changes load from a standbystate to a normal operation state.

While this invention has been described in connection with what ispresently considered to be practical exemplary embodiments, it is to beunderstood that the invention is not limited to the disclosed exemplaryembodiments, but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

DESCRIPTION OF SYMBOLS

-   -   10: fuel cell    -   200: stack    -   100: cell    -   300: power load    -   400: switch    -   500: monitoring terminal    -   600: controller    -   700: oscilloscope    -   800: data recorder    -   Vocv: open circuit voltage

What is claimed is:
 1. A method for calculating voltage loss of a fuelcell that includes a stack having cells, a power load using a currentand a voltage generated in the stack, a monitoring terminal connected tothe cells to sense the current and the voltage, a switch provided on acircuit that connects the power load and the stack, and a controllerconfigured to execute operations of the switch and the stack,comprising: sensing, by the controller, an open circuit voltagegenerated in the stack when the switch is opened; detecting, by thecontroller, an operation voltage and an operation current generated inthe stack when the switch is closed; calculating, by the controller, afirst change graph of voltage data over time using the voltage data andcurrent data from a time when the switch is opened when the switch isclosed, and sensing a first voltage of a point at which a trend line foran interval where the voltage data linearly varies with the time meetsthe first change graph; and calculating, by the controller, an ohmicresistance voltage loss using a difference value between the firstvoltage and the operation voltage.
 2. The method of claim 1, furthercomprising: calculating, by the controller, a second change graph of thevoltage data over square root of the time, and calculating a secondvoltage of a point at which a trend line for an interval where thevoltage data linearly varies with the square root time meets the secondchange graph; and calculating, by the controller, a mass transferresistance voltage loss using a difference value between the opencircuit voltage and the second voltage.
 3. The method of claim 2,further comprising: calculating, by the controller, an active resistancevoltage loss by subtracting the mass transfer resistance voltage lossand the ohmic resistance voltage loss from the open circuit voltage. 4.The method of claim 1, wherein the controller is configured to measurechanges in the voltage data and the current data with respect to thetime in a predetermined time unit using an oscilloscope or a datarecorder connected to the monitoring terminal.
 5. A method forcalculating voltage loss of a fuel cell that includes a stack havingcells, a power load using a current and a voltage generated in thestack, a monitoring terminal connected to the cells to sense the currentand the voltage, a switch provided on a circuit that connects the powerload and the stack, and a controller configured to execute operations ofthe switch and the stack, comprising: sensing, by the controller, anopen circuit voltage generated in the stack when the switch is opened;calculating, by the controller, a first change graph of voltage dataover time using the voltage data and current data generated from a timewhen the switch is closed when the switch is opened, and sensing ahighest first voltage in an interval where the voltage data linearlyvaries with the time; detecting, by the controller, an operation voltagegenerated in the stack when the switch is closed; and calculating, bythe controller, an ohmic resistance voltage loss using a differencevalue between the highest first voltage and the operation voltage. 6.The method of claim 5, further comprising: calculating, by thecontroller, a second change graph of the voltage data over square rootof the time, and calculating a lowest second voltage in an intervalwhere the voltage data linearly varies with the square root time; andcalculating, by the controller, a mass transfer resistance voltage lossusing a difference value between the open circuit voltage and the lowestsecond voltage.
 7. The method of claim 6, further comprising:calculating, by the controller, an active resistance voltage loss bysubtracting the mass transfer resistance voltage loss and the ohmicresistance voltage loss from the open circuit voltage.
 8. A method forcalculating a voltage loss of a power supply that includes a power loadusing a current and a voltage generated in the power supply, amonitoring terminal connected to the power supply to sense the currentand the voltage, a switch provided on a circuit that connects the powerload and the power supply, and a controller configured to executeoperations of the switch and the power supply, comprising: sensing, bythe controller, an open circuit voltage generated in the power supplywhen the switch is opened; sensing, by the controller, an operationvoltage and an operation current generated in the power supply when theswitch is closed; calculating, by the controller, a first change graphof voltage data over time using the voltage data and current data from atime when the switch is opened in a state where the switch is closed,and sensing a highest first voltage that corresponds to a point at whicha trend line for an interval where the voltage data linearly varies withthe time meets the first change graph; and calculating, by thecontroller, an ohmic resistance voltage loss using a difference valuebetween the highest first voltage and the operation voltage.
 9. Themethod of claim 8, further comprising: calculating, by the controller, asecond change graph of the voltage data over square root of the time,and calculating a lowest second voltage that corresponds to a point atwhich a trend line for an interval where the voltage data linearlyvaries with the square root time meets the second change graph; andcalculating, by the controller, a mass transfer resistance voltage lossusing a difference value between the open circuit voltage and the lowestsecond voltage.
 10. The method of claim 9, further comprising:calculating, by the controller, an active resistance voltage loss bysubtracting the mass transfer resistance voltage loss and the ohmicresistance voltage loss from the open circuit voltage.
 11. The method ofclaim 8, wherein the controller is configured to measure changes in thevoltage data and the current data with respect to the time in apredetermined time unit using an oscilloscope or a data recorderconnected to the monitoring terminal.
 12. A method for calculating avoltage loss of a power supply that includes a power load using acurrent and a voltage generated in the power supply, a monitoringterminal connected to the power supply to sense the current and thevoltage, a switch provided on a circuit that connects the power load andthe power supply, and a controller configured to execute operations ofthe switch and the power supply, comprising: sensing, by the controller,an open circuit voltage generated in the stack when the switch isopened; calculating, by the controller, a first change graph of voltagedata over time using the voltage data and current data generated from atime when the switch is closed in a state where the switch is opened,and sensing a highest first voltage in an interval where the voltagedata linearly varies with the time; sensing, by the controller, anoperation voltage generated in the stack when the switch is closed; andcalculating, by the controller, an ohmic resistance voltage loss using adifference value between the highest first voltage and the operationvoltage.
 13. The method of claim 12, further comprising: calculating, bythe controller, a second change graph of the voltage data over squareroot of the time, and calculating a lowest second voltage in an intervalwhere the voltage data linearly varies with the square root time; andcalculating, by the controller, a mass transfer resistance voltage lossusing a difference value between the open circuit voltage and the lowestsecond voltage.
 14. The method of claim 13, further comprising:calculating, by the controller, an active resistance voltage loss bysubtracting the mass transfer resistance voltage loss and the ohmicresistance voltage loss from the open circuit voltage.
 15. A systemperforming a method for calculating voltage loss of a fuel cell,comprising: a stack including a plurality of cells; a power load using acurrent and a voltage generated in the stack; a monitoring terminalconnected to the cells to sense the current and the voltage; a switchprovided on a circuit that connects the power load and the stack; and acontroller configured to: execute operations of the switch and thestack; sense an open circuit voltage generated in the stack when theswitch is opened; detect an operation voltage and an operation currentgenerated in the stack when the switch is closed; calculate a firstchange graph of voltage data over time using the voltage data andcurrent data from a time when the switch is opened in a state where theswitch is closed; sense a first voltage of a point at which a trend linefor an interval where the voltage data linearly varies with the timemeets the first change graph; and calculate an ohmic resistance voltageloss using a difference value between the first voltage and theoperation voltage.
 16. The system of claim 15, wherein the controller isconfigured to calculate a second change graph of the voltage data oversquare root of the time, calculate a second voltage of a point at whicha trend line for an interval where the voltage data linearly varies withthe square root time meets the second change graph, and calculate a masstransfer resistance voltage loss using a difference value between theopen circuit voltage and the second voltage.
 17. The system of claim 16,wherein the controller is configured to calculate an active resistancevoltage loss by subtracting the mass transfer resistance voltage lossand the ohmic resistance voltage loss from the open circuit voltage. 18.The system of claim 15, wherein the controller is configured to measurechanges in the voltage data and the current data with respect to thetime in a predetermined time unit using an oscilloscope or a datarecorder connected to the monitoring terminal.
 19. A system performing amethod for calculating voltage loss of a fuel cell, comprising: a stackincluding a plurality of cells; a power load using a current and avoltage generated in the stack; a monitoring terminal connected to thecells to sense the current and the voltage; a switch provided on acircuit that connects the power load and the stack; and a controllerconfigured to: control operations of the switch and the stack, sense anopen circuit voltage generated in the stack when the switch is opened;calculate a first change graph of voltage data over time using thevoltage data and current data generated from a time when the switch isclosed in a state where the switch is opened; sense a highest firstvoltage in an interval where the voltage data linearly varies with thetime; detect an operation voltage generated in the stack when the switchis closed; and calculate an ohmic resistance voltage loss using adifference value between the highest first voltage and the operationvoltage.
 20. The system of claim 19, wherein the controller isconfigured to: calculate a second change graph of the voltage data oversquare root of the time; calculate a lowest second voltage in aninterval where the voltage data linearly varies with the square roottime; calculate a mass transfer resistance voltage loss using adifference value between the open circuit voltage and the lowest secondvoltage; and calculate an active resistance voltage loss by subtractingthe mass transfer resistance voltage loss and the ohmic resistancevoltage loss from the open circuit voltage.